Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Chattanooga to New Bern as you normally would.
Leaving on a Wednesday is a viable option for saving on travel. Heavily demanded days of the week can typically drive up the prices you see. Booking your travel for a less competitive day can save up to 29% on the overall cost on flights from Chattanooga to New Bern.